A typical ice shaver or crusher according to the prior art comprises a mechanical cutting member (e.g., a set of blades or teeth) coupled to a power source (e.g., an electric motor) for driving the cutting member. A typical food processor for domestic use conventionally comprises a set of rotary blades driven by an electric motor. However, domestic food processors are not designed (and are generally not suitable) as a system for use in shaving or crushing ice, because conventional food processors are not robust enough to drive a set of rotary blades quickly and continuously through solid ice without producing large amounts of excess waste due to melting. In addition, conventional food processors generally provide no means to handle waste due to melting or spills.